Introduction to Computing

CPIT $201-$ Homework $2-$ Due September $20$

Store $xx$ in an $8-$bit memory location using unsigned representation? Show your work?

$[0\mathrm{.}5$ point each$)$

$xx=(???{)}_2$

Store $-xx$ in an $8-$bit memory location using sign$-$and$-$magnitude representation? Show

your work?

$-xx=(???{)}_2$

Store $-$ XX in an $8-$bit memory location using two's complement representation? Show

your work?

$-xx=(???{)}_2$

Where $xx=$ the last $2$ digits of your student number. Example $-xx=-76.$ If you have

one$/$t wo digits $0$ s$,$ use $\frac{5}{55}$ instead of zeros digits $x\frac{5}{5}\frac{x}{55}.$

Retrieve the integer that stored as $11101111$ in memory in unsigned format? Show your

work?

$(11101111{)}_2=(???)$

Retrieve the integer that stored as $11101111$ in memory in sign$-$and$-$magnitude format?

Show your work?

$(11101111{)}_2=(???)$

Retrieve the integer that stored as $10110101$ in memory in two's complement format?

Show your work?

$(10110101{)}_2=(???)$

Using floating$-$point representation $($IEEE$\_127)($single precision$),$ show the process how

$(-xx.xx)$ is represented?

Where $xx.xx=$ the last $2$ digits of your student number. Example $-xx.xx=-76\mathrm{.}76($no

more than $4$ digits in the fractional parts$)$

The number $(47802058)16$ is stored in floating$-$point representation $($IEEE$\_127).$ Show

the process to retr$$ve the or$$ginal decimal number?

Hint: $1)$ convert hexadecimal to binary

use IEEE standards

Use the last digit of your student number as $x-$bit memory location in two's complement.

a$)$ How many different patterns $($symbols$)$ can be represented using $x$ bits?

b$)$ show the range for all numbers that can be represented $($minimum and maximum

values$)?$

c$)$ Show the binary representation of the first two numbers and the last two numbers?

d$)$ Discuss when an overflow would happen?

If $x2,$ use $x=5.$